Several issues related to the development of mathematical ability remain unanswered. Project 5, in collaboration with the other projects in this proposal, will address several questions about early math development. The aims of this project are to investigate the developmental trajectories of informal preschool math skills, their relation to math outcomes and math skills at school-age, and the cognitive competencies that underlie preschool math abilities. In addition, the project investigates relations between growth in math skills and the development of literacy, language, and social skills. Early math skills including counting knowledge and procedures, nonverbal and verbal problem solving involving addition and subtraction, conceptual math knowledge such as inversion, and geometric reasoning and measurement skills, are assessed during the preschool years in the context of an integrated preschool curriculum. These informal math skills and their underlying cognitive competencies will be related to math outcomes at the end of the pre-k year (Project 1 cohort), and to math outcomes and achievement in domains such as arithmetic fact retrieval, calculation principles and procedures, geometry, word problems, and measurement, at the end of kindergarten and grade 1. Relations between the development of informal mathematical skills and general cognitive competencies, including working memory, spatial ability, fine motor skill, and phonological skills will be tested. In relation to Projects 1 and 2, intervention-related effects on growth in informal mathematical skills and their related cognitive competencies will be examined. In relation to Projects 3 and 4, hypotheses relating the development of particular informal math skills to concurrently developing language and social skills will be tested. The approach is innovative in that it involves model-driven, longitudinal assessment of core informal mathematical skills and supporting cognitive competencies in young children in which relations to early literacy, language and social development can also be addressed.